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- Samuli Ikonen, Jari Toivanen
- Appl. Math. Lett.
- 2004

We propose an iterative method for pricing American options under jumpdiffusion models. A finite difference discretization is performed on the partial integro-differential equation, and the American option pricing problem is formulated as a linear complementarity problem (LCP). Jump-diffusion models include an integral term, which causes the resulting… (More)

Efficient numerical methods for pricing American options using Heston’s stochastic volatility model is proposed. Based on this model the price of a European option can be obtained by solving a two-dimensional parabolic partial differential equation. For an American option the early exercise possibility leads to a lower bound for the price of the option.… (More)

- Ferrante Neri, Jari Toivanen, Giuseppe Leonardo Cascella, Yew-Soon Ong
- IEEE/ACM Transactions on Computational Biology…
- 2007

This paper proposes a period representation for modeling the multidrug HIV therapies and an Adaptive Multimeme Algorithm (AMmA) for designing the optimal therapy. The period representation offers benefits in terms of flexibility and reduction in dimensionality compared to the binary representation. The AMmA is a memetic algorithm which employs a list of… (More)

Five numerical methods for pricing American put options under Heston’s stochastic volatility model are described and compared. The option prices are obtained as the solution of a two-dimensional parabolic partial differential inequality. A finite difference discretization on nonuniform grids leading to linear complementarity problems with M -matrices is… (More)

- Tuomas Airaksinen, Erkki Heikkola, Anssi Pennanen, Jari Toivanen
- J. Comput. Physics
- 2007

Apreconditioner defined by an algebraicmultigrid cycle for a dampedHelmholtz operator is proposed for the Helmholtz equation. This approach is wellsuited for acoustic scattering problems in complicated computational domains and with varying material properties. The spectral properties of the preconditioned systems and the convergence of the GMRESmethod are… (More)

- S. Ikonen, J. Toivanen
- 2004

Abstract. Option pricing models with a stochastic volatility are more realistic than the Black-Scholes model which uses a constant volatility. The prices of options based on such models can be obtained by solving a parabolic partial differential equation. Particularly, we consider the model presented by Heston. The variables in these problems are the time,… (More)

- Ferrante Neri, Jari Toivanen, Raino A. E. Mäkinen
- Applied Intelligence
- 2007

This paper proposes a novel Memetic Algorithm consisting of an Adaptive Evolutionary Algorithm (AEA) with three Intelligent Mutation Local Searchers (IMLSs) for designing optimal multidrug Structured Treatment Interruption (STI) therapies for Human Immunodeficiency Virus (HIV) infection. The AEA is an evolutionary algorithm with a dynamic parameter setting.… (More)

- Jari Toivanen
- SIAM J. Scientific Computing
- 2008

Numerical methods are developed for pricing European and American options under Kou’s jump-diffusion model which assumes the price of the underlying asset to behave like a geometrical Brownian motion with a drift and jumps whose size is log-double-exponentially distributed. The price of a European option is given by a partial integro-differential equation… (More)

Numerical solution methods for pricing American options are considered. We propose a second-order accurate Runge-Kutta scheme for the time discretization of the Black-Scholes partial differential equation with an early exercise constraint. We reformulate the algorithm introduced by Brennan and Schwartz into a simple form using a LU decomposition and a… (More)